Superstar Investors

Many famous investors are outspoken about their investment philosophies, and carefully apply them to a select number of securities. In this Alternative Thinking, we seek to apply their wisdom systematically; to ask whether their philosophies applied broadly might still generate “alpha”.11CloseWe are not the first to try to demystify successful investment strategies: for other studies see Siegel, Kroner and Clifford (2001) for a range of public and private funds and institutions; Gergaud and Ziemba (2012); Pedersen (2015) for hedge fund managers; Frazzini, Kabiller and Pedersen (2012) for a deeper treatment of Berkshire Hathaway than covered in this article; Hurst, Ooi and Pedersen (2013) for trend-following strategies; and Chambers, Dimson and Foo (2015) for Keynes. Additionally, see Asness et al. (2015) for more background on the styles underlying our analysis.

Our analysis suggests there are many ways to achieve long-run investment success. The takeaway for investors is to identify structural edges and commit to seeing them through inevitable periods of underperformance. As each of our superstars shows, “merely good” edges over time may compound to great long-term performance.

TABLE OF CONTENTS

Executive Summary

Much has been said about superstar investors22CloseThere is no strict definition of who qualifies as a “superstar investor”, but the ones in this article are investors we deem to be well-known, successful managers with decades-long track records, and cover a diverse range of asset classes. We may analyze more investors we deem to be “superstars” in future research.
and their investment styles, but there has been much less empirical analysis to explain their performance.

Our findings suggest that success for many great investors is not luck or chance, but in large part reward for long-term exposure to factors that have historically produced excess returns.

Thus, a key takeaway for investors is to identify structural edges (factor tilts or otherwise) and then have the patience to stick with them for the long term.

Though our results may seem compelling, we have the clear benefit of hindsight. Any “alpha” that comes out of our analysis is thus understated. These great investors “figured it out” first, had the ability to stick to their philosophies, and rightly deserve their reputations.

Introduction

Ben Graham taught me 45 years ago that in investing it is not necessary to do extraordinary things to get extraordinary results.”

— Warren Buffett, Berkshire Hathaway Inc., Annual Report, 1994.

One of the biggest financial “innovations” in the past few years is factor — or style — investing, but it’s really not much of an innovation. This type of investing typically applies well-known, time-tested principles in a rules-based manner. In this issue of Alternative Thinking, we show how four very different, extraordinary track records — Berkshire Hathaway, PIMCO’s Total Return Fund in the Gross era, George Soros’s Quantum Fund, and Fidelity’s Magellan Fund under Peter Lynch — can be viewed as an expression of a handful of systematic styles.
33CloseWe note upfront that our focus is on performance, and not how much of it a specific portfolio manager was responsible for. In other words, we cannot say how much our Berkshire Hathaway results reflect the contributions of Warren Buffett versus Charlie Munger, or how much of Quantum Fund’s results reflect decisions by George Soros versus Stanley Druckenmiller, or how much the many colleagues of Bill Gross and Peter Lynch at PIMCO and Fidelity contributed. Although these names are generally associated with these successful track records, we recognize that success is often the result of a team effort.44CloseAn important caveat is the factors used here are gross of fees, trading costs, and other real-world frictions; and thus mechanically understate the “alpha” reported for these superstar track records. For an analysis of trading costs of factors such as the ones covered here, refer to Frazzini, Israel and Moskowitz (2012). (Additionally, results of any regression analysis are sensitive to factor construction and specifications, which lead to either over- or understated alphas. For more on this point, we refer readers to Israel and Ross (2015).) Two other effects are worth noting – each influences alpha in the opposite direction. The first is that any study such as this one has (unavoidable) hindsight bias when choosing which factors to include. This results in some overfitting and “over-explanation” of these superstars’ track records, and thus will understate alpha. The second effect leads to alpha being overstated. How? This article picks four out of thousands of managers who did very, very well. Some readers may argue that we can’t be sure that these managers weren’t just very, very lucky, and that their true alpha is meaningfully smaller than what we estimate.

Berkshire Hathaway — Value, Quality, Low-Risk (and Leverage)

Whether we’re talking about socks or stocks, I like buying quality merchandise when it is marked down.”

— Warren Buffett, Berkshire Hathaway Inc., Annual Report, 2008.

1. Berkshire Hathaway

Value, Quality, Low-Risk (and Leverage)

Source: AQR, CRSP (for BRK data), Kenneth French Data Library (for Equities, which are CRSP cap-weighted returns; and risk-free rate, which is 1-month Treasuries). For consistency, we’ve chosen the CRSP cap-weighted index to represent U.S. Equities throughout this article. Returns are excess of cash throughout this article. Past performance is not a guarantee of future performance; please read important disclosures at the end of this presentation. *Returns in all exhibits are excess of cash, unless stated otherwise. Factor returns are all gross of fees and transactions costs. **U.S. Equities throughout this article are the CRSP cap-weighted equity market factor from Kenneth French’s website.

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We start with Berkshire Hathaway (BRK) over the period from January 1977 to May 2016. We note that while BRK’s average annual return over this long period is much higher than that of the U.S. stock market (excess of cash returns of 17.6% versus 6.9%), it also came with meaningfully higher volatility. Adjusting for volatility, BRK realized a Sharpe ratio of 0.74, compared to 0.45 for the broad U.S. market.55CloseWhile a 0.74 Sharpe ratio might not seem stratospheric, it is higher than that of any other stock or mutual fund with a history of more than 30 years.
BRK has also produced significant alpha to traditional risk factors. However, we find that this alpha becomes statistically insignificant when controlling for some of the investment styles Buffett describes in his writings. Specifically, our “Buffett factors” for this analysis are:66CloseSee Appendix for details on factor construction.

Our regression results are presented in the table at the left of Exhibit 1. Each of the “Buffett factors” used are statistically significant (i.e., the t-stats are all larger than 2), suggesting that each of these investment styles played a role in BRK’s success. To provide a sense of magnitudes, we also show an attribution (based on the regression results) in the chart at the right of Exhibit 1.99CloseReturn attributions are the factor coefficients multiplied by the average factor premium.

All variables here, and in subsequent exhibits, are excess of cash, unless stated otherwise. The market beta (0.98) is not statistically different than 1. The relatively low R2 is due in part to high idiosyncratic volatility of Berkshire Hathaway stock compared to the broad factors used in the regression.

*Not statistically significant (i.e., t-stat less than 2). Contributions shown above are the product of the coefficients in the table and the average premium for each factor over the period January 1977 - May 2016.

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One of the ways that Berkshire Hathaway was able to add so much return above that of the market is Berkshire’s access to cheap leverage via its insurance business, allowing it to harvest greater amounts of these style exposures than most traditional investors could.1010CloseFor more, see Frazzini, Kabiller and Pedersen (2013). The authors use balance sheet data from Compustat/XpressFeed, hand-collected annual reports, holdings data for Berkshire Hathaway from Thomson Financial Institutional (13F) Holding Database (based on Berkshire’s SEC filings), and the size and cost of the insurance float from hand-collected comments in Berkshire Hathaway’s annual reports to estimate — among other characteristics — the leverage employed by Berkshire Hathaway, and the additional returns achieved via this leverage. Past performance is not a guarantee of future performance.
To get an idea of magnitude, for every dollar invested in BRK from 1977 through May 2016, investors on average got about $1 exposure to the stock market (the market beta) and an additional $1.3 dollars exposure to the other factor premia shown in Exhibit 1 (the sum of the betas to the value, low-risk and quality factors from the regression).

PIMCO’s Total Return Fund — High Yield Credit, Short Maturity, Short Volatility

On a somewhat technical basis, my/our firm’s tendency to sell volatility and earn ‘carry’ in a number of forms—
outright through options and futures, in the mortgage market via prepayment risk, and on the curve via bullets
and roll down as opposed to barbells with substandard carry—has been rewarded over long periods of time.”

Source: AQR, CRSP. Risk free rate is 1-month Treasury bills. Past performance is not a guarantee of future performance; please read important disclosures at the end of this presentation. *Our analysis starts in 1994 due to availability of factor data. *Our analysis starts in 1994 due to availability of factor data.

*The “market beta” is also statistically larger than 1.0 (with a t-stat of 2.32), suggesting that a portion of excess returns was also likely from taking more duration risk on average. Note: all data in this exhibit are gross of fees. Explanatory variables are gross of transactions costs. Market is the Barclays U.S. Aggregate Bond Index, excess of cash, credit is 5-year US High Yield CDX, short maturity (rank-sorted portfolio of negative maturity on U.S. 2/5/10/20-year bond futures), and short volatility (the returns from selling 1-month, 30-delta strangles on 10-year Treasury futures, delta-hedged).

*Not statistically significant.Contributions shown above are the product of the coefficients in the table and the average premium for each factor over the period January 1994 - September 2014.

The PIMCO Total Return Fund (TRF) is arguably the best-known, and until recently the largest, bond fund in the world.1212CloseThe PIMCO Total Return Fund hit a peak of $292.9 billion in assets under management in April 2013, but was overtaken by Vanguard’s Total Bond Market Index Fund in April 2015.
Bill Gross was at the helm of TRF since its inception in 1987 until leaving PIMCO in 2014. Though Gross wasn’t the sole portfolio manager, many of his well-read Investment Outlooks (including the one quoted above) described what TRF did to try to outperform the broader bond market.1313CloseInvestment outlooks available at: https://www.pimco.com/insights/economic-and-market-commentary

Gross’s writings describe a long-run strategy of both harvesting many sources of returns, as well as trying to time them. For the former, many of these return sources were different forms of carry trades, summed up neatly by many bond managers as “own short-maturity BBBs”, a well-known strategy for decades.1414CloseOf course, it didn’t have to be BBB-rated debt, but the idea was that shortermaturity,lower-rated debt was generally a “smart trade”.
While TRF’s actual holdings were far broader (including mortgages, linkers and emerging market debt1515CloseSource: Morningstar.
), we find much of TRF’s average excess return can be explained by exposure to shorter maturity names (using derivatives to achieve similar duration to the benchmark, the Barclay’s U.S. Aggregate), and picking up credit risk.

Gross was also known to focus on another source of excess returns: short volatility. This was pursued in many ways, including exposure to mortgages, but we can express the same general idea of capturing the volatility risk premium by being short fixed income options.1616CloseThe volatility risk premium is compensation paid by option buyers (i.e., insurance seekers) to sellers for bearing undesirable downside risk, and is typically measured by the difference between an option’s implied volatility and its underlying asset’s realized volatility. For more on this premium in multiple asset class contexts, see the 4Q2015 Alternative Thinking.

Thus, to test if a “systematic Gross strategy” can explain the average returns of TRF, we use the following four factors (See Appendix for details on factor construction.):

Market: Barclays U.S. Aggregate Bond Index

Credit: 5-year U.S. High Yield CDX

Low-Risk: duration neutral factor that is long 2- and 5-year, versus short 10- and 30-year U.S. bond futures1717CloseMore plainly, a factor that is long shorter duration bonds and short longer duration bonds (the “Betting Against Beta” [BAB] factor is the analogous concept in equities).

A regression against TRF shows that these factors can help explain much of the average returns, with statistically significant exposures on each factor (see Exhibit 2 for statistics and an illustrative return attribution).

We try to catch new trends early and in later stages we try to catch trend reversals. Therefore, we tend to stabilize
rather than destabilize the market. We are not doing this as a public service. It is our style of making money.”

Source: AQR, HFR. Risk-free rate is 1-month Treasuries For consistency, we’ve chosen the CRSP cap-weighted index to represent U.S. Equities throughout this article. Past performance is not a guarantee of future performance; please read important disclosures at the end of this presentation. *Unfortunately, due to data availability we have “only” 20 years of data to analyze.

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George Soros is not only one of the first but also arguably one of the most successful hedge fund managers of all time. He focuses on global macro strategies, and is particularly well known as a currency trader. Among his most successful funds is the Quantum Fund, perhaps best known for short-selling the British pound during the 1992 U.K. currency crisis (a trade attributed to Soros and Stanley Druckenmiller), which made around $1B profit and led to Soros’s reputation as “the man who broke the Bank of England”. Soros is known for developing a theory of boom/bust cycles and reflexivity, based on negative and positive feedback between prices and fundamentals (emphasizing the role of self-reinforcing positive feedback). Given his focuses on trends and currencies, our “Quantum factors” are:2020CloseSee Appendix for details on factor construction.

In stocks, the UMD factor from Kenneth French’s data library2121CloseThough Soros did trade Japanese and European stocks, we use only a U.S. equities momentum factor here, given his focus on U.S. stocks.

In macro asset classes, the Time Series Momentum (TSMOM) factor2222CloseAs defined in Hurst, Ooi and Pedersen (2014).
from AQR’s data library

Exhibit 3:

The Quantum Fund, March 1985-May 2004 Regression Statistics

Source: HFR. Note: Quantum Fund returns are net of fees and only cover a portion of the full track record (due to data availability). Explanatory variables are gross of fees and transactions costs (which drives the alpha in the regression lower).

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Exhibit 3:

The Quantum Fund, March 1985-May 2004 Regression Statistics

*Not statistically significant. +Fundamental momentum, as opposed to traditional price-based momentum (see footnote 29). Contributions shown above are the product of the coefficients in the table and the average premium for each factor over the period March 1985 - May 2004.

Exhibit 3 shows results of our regression analysis (table) and a regression-based attribution of Quantum’s average returns (bar chart). Not surprisingly, trend/momentum factors go a long way in explaining the average returns over the period.

Magellan — Small Stocks, Momentum… and a Lot of Alpha

Peter Lynch, 25 Years Later: It’s Not Just ‘Invest in What You Know’ The onetime mutual-fund rock star says the famous advice isn’t quite so simple
— Article title from the Wall Street Journal, Dec 6, 2015

4. Magellan

Small Stocks, Momentum… and a Lot of Alpha

Source: AQR, CRSP, Morningstar. Risk-free rate is 1-month Treasuries. For consistency, we’ve chosen the CRSP cap-weighted index to represent U.S. Equities throughout this article. Past performance is not a guarantee of future performance; please read important disclosures at the end of this presentation.

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Peter Lynch was at the helm of Fidelity’s Magellan Fund from May 1977 to May 1990, over which time the mutual fund grew from approximately $20M to $14B (reflecting both returns and inflows), and posted an average excess of cash return of 21% (compared to the stock market’s 7% excess return over the same period).2525CloseAUM figures from Morningstar.

Like other superstars covered here, Lynch was public about his investment philosophy, having authored multiple books on the topic.2626CloseIncluding (subsequently to the period covered here) in books, such as Beating the Street (1994), and One Up on Wall Street: How to Use What You Already Know to Make Money in the Market (2000).
Yet, Lynch’s philosophy was arguably less parsimonious than that of the other superstars: he had various checklists for various categories of companies2727CloseE.g., see Chapter 15 of Beating the Street.
, making the task of evaluating Magellan’s track record via broad factors more difficult (and maybe less relevant).

Exhibit 4:

The Magellan Fund, May 1977-May 1990 Regression Statistics

Note: all data in this exhibit are gross of fees. Explanatory variables are gross of transactions costs. Market (EQ) is the CRSP cap-weighted stock market index, excess of cash; Market (FI) is the Barclays U.S. Aggregate Bond Index, excess of cash; Size and Value are the SMB and HML factors, respectively, as defined in Fama and French (1992); Momentum is the UMD momentum factor; Quality is the “Quality minus Junk” factor as defined in Asness, Frazzini and Pedersen (2014); Low-Risk is the “Betting-Against-Beta” factor as defined in Frazzini and Pedersen (2014).

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Without a straightforward mapping from philosophy to wellknown factors, we instead include some of the most-used factors from academia.2828CloseWe are fully cognizant of the risk of data-mining, given Lynch’s investment philosophies don’t map strongly to these standard factors. Note that these are all U.S. factors, given Magellan’s focus on U.S. markets.
Thus our “Lynch factors” are:2929CloseSee Appendix for details on factor construction.

Market: both the U.S. equity market factor from Kenneth French’s data library and the Barclays U.S. Aggregate Bond Index3030CloseMagellan’s investment policies permitted allocations to “so-called ‘defensive securities,’ including fixed-income securities of all types and U.S. government obligations”. For instance, corporate and treasury bonds represented 15% of Magellan’s assets as of 9/30/1982.

Size: the SMB factor from Kenneth French’s data library

Value: the HML factor from Kenneth French’s data library

Momentum: the UMD factor from Kenneth French’s data library

Quality: the QMJ factor from AQR’s data library

Low-Risk: the BAB factor from AQR’s data library

Our findings are presented in Exhibit 4. Part of Magellan’s outperformance seems to be from taking more risk than the market3131CloseThe beta of 1.16 is statistically higher than 1.0, with a t-stat of 3.91.
, and harvesting small cap and momentum premia. We also find some exposure to the value premium, but smaller in magnitude (and resulting average returns, as shown in the attribution chart). Although exposure to the quality premium is not statistically significant (i.e., the t-stat is below 2), we note that even when applied systematically, “quality” is among the most heterogeneous investment styles, and

Exhibit 4:

The Magellan Fund, May 1977-May 1990 Regression Statistics

*Not statistically significant with 95% confidence. Contributions shown above are the product of the coefficients in the table and the average premium for each factor over the period May 1977 - May 1990.

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thus may be harder to measure. Finally, we note that Lynch’s impressive performance appears to have been in spite of negative exposure to the low-risk premium (unlike for Buffett, who harvested it).

However, despite the plethora of factors examined here, the headline from this analysis might be that Magellan still posted more than 8% “alpha” on average each year for 13 years. Capping it off, Lynch is famous for the rare feat of having left at the top — his successors at Magellan have had a much more typical track record (in the thirteen years following Lynch’s career there, Magellan’s alpha relative to the equity market factor has been indistinguishable from zero).3232CloseOver the period May 1990 - Dec 2012, using the same U.S. Equities factor as in the previous analysis. Interestingly, the beta to the equity market over this period is still above 1.0 (as it was during the Lynch era).

Exhibit 5:

The Quantum Fund: On Average, Successful Market Timing

Source: HFR, AQR. The chart above represents Quantum’s 36-month rolling beta to equities (the CRSP cap-weighted equity factor) alongside market returns over the period 1988-2003. Past performance is not a guarantee of future performance. Please read important disclosures in the Appendix. The average beta is from the full-sample regression, not the average of the 36-month market beta line.

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What About Market Timing?

Berkshire Hathaway

BRK’s equity market exposure, or beta, in general has fallen over 40 years (which means less returns from the equity risk premium). But this beta has varied meaningfully around its long-term decline, which leads to an interesting question: has tactical market exposure been an additional source of returns for BRK? One way to test this is to examine the “tactical beta” (which we define as the difference between the rolling 36-month beta and the full-sample beta).3333CloseSpecifically, for all track records, we look at the correlation between 36-month “tactical beta” and contemporaneous market return. “Tactical beta” is the difference between trailing 36-month beta and average (full sample) beta. We also analyzed tactical market exposures over a shorter horizon, using rolling 24-month observations, and find the same general results (though not shown here for brevity).
If this tactical beta was higher/lower when the market performed well/poorly, that would imply market timing skill.

The data shows no meaningful correlation between changes in market exposure and market returns, suggesting that market timing — whether intentional or not — has not been a source of “alpha” for BRK. In other words, BRK’s impressive long-term track record may be less about market timing and more about exposure to well-rewarded investment styles.3434CloseWhich is not surprising, given how much of BRK’s average excess returns in Exhibit 1 could be attributed to these styles.

PIMCO Total Return Fund in the Gross Era

Our analysis of TRF did not include any time-variation in exposures, and thus already implies that tactical timing may have been less important to TRF’s success than many investors assume. However, we know TRF timed markets, famously by tactically timing Treasury duration (and on occasion U.S. dollar movements), and much of PIMCO’s communication focused on secular and cyclical bets.

We find mixed success for “beta timing”: when it comes to timing exposure to the benchmark (in this case, duration timing), we find no correlation between market timing decisions and over/underperformance of the benchmark.3535CloseThe specific benchmark we use here is the Barclays U.S. Aggregate.

In other words, duration timing — while certainly a feature of TRF — did not seem to add much value on average. In contrast, we find that credit timing may have added value.3636CloseMore specifically, we find a 0.5 correlation between changes in 36-month rolling betas to contemporaneous 36-month high yield factor (5-year U.S. High Yield CDX) returns, and a 0.3 correlation between changes in 24-month rolling betas to contemporaneous 24-month high yield factor returns. Past performance is not a guarantee of future performance.
Specifically, TRF increased its exposure to the credit premium following the financial crisis (a period over which credit performed well).

Hedge fund managers as a group are long-equity biased3838CloseWe’ve highlighted this going back at least 15 years — see, e.g., Asness, Krail and Liew (2001).
, and Soros seems to be no exception, with the Quantum Fund posting an average market beta of 0.6 over this 20-year period. However, the beta varies considerably around this average (see Exhibit 5) — over some 3-year periods, the Quantum Fund had a beta in excess of 1, and in others, the beta was negative.

Did this market timing help? Exhibit 5 provides a simple way of approaching this question, by graphing Quantum’s 36-month rolling beta to equities (gray) alongside market returns (purple) over those same periods. Visually, the decision to decrease market exposure in the early 1990s appears to have detracted value (as equity market returns were strongly positive over that period), and the decision to increase market exposure seems to have positively contributed in the late 1990s during the tech bubble. Over the 20-year sample, we find a positive correlation between his “tactical beta”47 and returns, suggesting that Soros was able to add alpha via market timing.3939CloseOur data extends only to 2004, and misses when Soros returned to the helm of Quantum to navigate through the financial crisis: “my coming out of retirement, or semiretirement, to take an active role in anticipation of the financial crisis of 2008… [Quantum] was a pretty large fund, where the positions tended to be on the long side so I opened a macro account where I hedged, basically, the positions of others and took positions that were net/net short” (Interview with George Soros in Efficiently Inefficient (2015)).

Magellan in the Lynch Era

Given the magnitude of the alpha in the Magellan regression and attribution, it’s natural to turn to market timing as a potential source of excess returns. However, our results suggest little (if any) timing benefit, suggesting that security selection was a much greater source of Magellan’s success than was market timing.

Conclusion: Learning from the Masters

But let me admit something… All of us, even the old guys like Buffett, Soros, Fuss, yeah — me too, have cut our teeth during perhaps a most advantageous period of time, the most attractive epoch, that an investor could experience. Since the early 1970s… an investor that took marginal risk, levered it wisely and was conveniently sheltered from periodic bouts of deleveraging or asset withdrawals could, and in some cases, was rewarded with the crown of ‘greatness.’

What can investors take away from this analysis? First, for many great investors success is not luck or chance, but reward for long-term exposure to styles that have historically produced excess returns. Second, the styles we analyzed have been successful in many contexts — from fixed income portfolios to global macro hedge funds.4040CloseSee Asness, Ilmanen, Israel and Moskowitz (2015) for decades of evidence across multiple regions and asset classes.
This has clear implications for manager selection, regardless of whether the manager is fundamental or quantitative, traditional or alternative: investors should understand which (if any) styles are part of a manager’s process, and decide whether there are positive expected returns associated with those styles. Third, styles alone aren’t sufficient for success; they also require patience, ability and a long-horizon to stick with them.

So what about “alpha”? As Lynch shows, the onslaught of common (and some less common) factors still can’t explain all of his outperformance — even with the benefit of hindsight. We are forced to conclude — at least for now — that part of Magellan’s success was more than just compensation for style exposure. Namely, a meaningful portion of those excess returns was, and probably still is, “alpha.”

What about for the other managers, the ones with no “alpha” in our regressions? They too had “alpha”, but relative to what we knew about markets back when they were actually investing. Surely that should count. Bigger picture, regardless of whether outperformance comes from alpha or style “betas”, investors today face low expected returns across traditional asset classes.4141CloseSee Asness and Ilmanen (2012); also AQR Alternative Thinking 1Q2016 for more recent capital market assumptions; and from a defined contribution perspective Ilmanen, Rauseo and Truax (2016).
Given these headwinds, any additional non-market sources of returns may be especially valuable. While historically the main way to outperform was via alpha or simply taking more risk, investors now have access to a suite of other style premia; potentially allowing for multiple paths to long-term success.

Market (as described in Kenneth French’s Data Library): Rm-Rf, the excess return on the market, value-weight return of all CRSP firms incorporated in the U.S. and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 or 11 at the beginning of month, good shares and price data at the beginning of t, and good return data for t minus the one-month Treasury bill rate (from Ibbotson Associates). See Fama and French, 1993, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics, for a complete description of the factor returns.

Value (as described in Kenneth French’s Data Library): HML (High Minus Low) is the average return on the two value portfolios minus the average return on the two growth portfolios, HML = 1/2 (Small Value + Big Value) - 1/2 (Small Growth + Big Growth). HMLincludes for July of year t to June of t+1 all NYSE, AMEX, and NASDAQ stocks for which we have market equity data for December of t-1 and June of t, and (positive) book equity data for t-1.

Low-Risk: the “Betting-Against-Beta” (BAB) factor from AQR’s data library, as defined in Frazzini and Pedersen (2014). BAB factors are portfolios that are long low-beta securities and that short-sell high-beta. To construct each BAB factor, all securities in a country are ranked in ascending order on the basis of their estimated beta and the ranked securities are assigned to one of two portfolios: low-beta and high-beta. In each portfolio, securities are weighted by the ranked betas (lower-beta securities have larger weights in the low-beta portfolio and higher-beta securities have larger weights in the high-beta portfolio). The portfolios are rebalanced every calendar month. To construct the BAB factor, both portfolios are rescaled to have a beta of one at portfolio formation. The BAB is the self-financing zero-beta portfolio that is long the low-beta portfolio and that short-sells the high-beta portfolio

Quality: the “Quality-Minus-Junk” (QMJ) factor from AQR’s data library, as defined in Asness, Frazzini and Pedersen (2014). The Quality Score is the average of four aspects of quality: Profitability, Growth, Safety and Payout. We use a broad set of measures to compute each of four aspects of quality; the score for each aspect is the average of the individual z-scores of the underlying measure. Each variable is converted each month into ranks and standardized to obtain the z-score. 1) Profitability is measured by: Gross profits over assets, return on equity, return on assets, cash flow over assets, gross margin, and the fraction of earnings composed of cash. 2) Growth is measured by: The five-year prior growth in profitability, averaged across the measures of profitability. 3) Safety is defined as: Companies with low beta, low idiosyncratic volatility, low leverage, low bankruptcy risk and low ROE volatility. 4) Payout is defined using: Equity and debt net issuance and total net payout over profits. QMJ factors are constructed as the intersection of six value-weighted portfolios formed on size and quality. At the end of each calendar month, we assign stocks to two size-sorted portfolios based on their market capitalization. For U.S. securities, the size breakpoint is the median NYSE market equity. We use conditional sorts, first sorting on size, then on quality. Portfolios are value-weighted, refreshed every calendar month, and rebalanced every calendar month to maintain value weights. The QMJ factor return is the average return on the two high-quality portfolios minus the average return on the two low-quality (junk) portfolios.

Short Maturity: We rank 2-year, 5-year, 10-year, and 20-year U.S. bond futures by their respective durations. The portfolio goes long the futures whose durations are below average, and short the futures with durations above average. Finally, the positions are re-scaled to be duration-neutral.

Short Volatility: The returns from selling a 1-month maturity, 30-delta strangle (i.e., selling a put and a call option), delta hedged option on U.S. 10-year bond futures.

For Quantum:

Market: same as used for the Berkshire Hathaway analysis.

Trend

In stocks: the UMD factor (as described in Kenneth French’s Data Library): is constructed monthly, using the intersections of 2 portfolios formed on size (market equity, ME) and 3 portfolios formed on prior (2-12) return. The monthly size breakpoint is the median NYSE market equity. The monthly prior (2-12) return breakpoints are the 30th and 70th NYSE percentiles.

In macro asset classes: the Time Series Momentum (TSMOM) factor from the AQR data library. We construct a return series for each of the underlying instruments as follows: Each day, we compute the daily excess return of the most liquid futures contract (typically the nearest or next nearest to delivery contract), and then compound the daily returns to a total return annualized volatility of 40%. (Note: the choice of 40% is inconsequential, but it makes it easier to intuitively compare our portfolios to others in the literature, as it has an annualized volatility of about 12% per year over the sample period which is roughly the level of volatility exhibited by other factors such as those of Fama and French (1993) and Asness, Moskowitz and Pedersen (2010)). For more on this factor, see Moskowitz, Tobias J., Yao Hua Ooi and Lasse. H. Pedersen, 2012, “Time Series Momentum,” Journal of Financial Economics, 104(2), 228-250).

Currencies

Momentum: a “fundamental” measure using trailing 1-year equity market momentum. We rank the 12-month equity returns for every country in our region (AU, BD, CN, JP, NW, NZ, SD, SW, UK, and US). The portfolio goes long the currency of any country whose equity return ranks above average, and goes short the below average countries. Finally, the positions are re-scaled to be dollar-neutral.

Value: purchasing power parity applied across G10 markets. We rank each country by their real exchange rate (spot rate divided by purchasing power parity). The portfolio goes long the currencies of the countries whose real exchange rates rank above average, and goes short the below average countries. Finally, the positions are re-scaled to be dollar-neutral.

For Magellan in the Lynch Era:

Market: ––Equities: the same as used for the Berkshire Hathaway analysis. ––Fixed income: the same as used for the PIMCO Total Return analysis.

Size: the SMB factor (as described in Kenneth French’s Data Library): is the average return on the three small portfolios minus the average return on the three big portfolios: SMB = 1/3 (Small Value + Small Neutral + Small Growth) – 1/3 (Big Value + Big Neutral + Big Growth). See Fama and French, 1993, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics, for a complete description of the factor returns.

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